Local-in-time well-posedness for compressible MHD boundary layer |
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Authors: | Yongting Huang Cheng-Jie Liu Tong Yang |
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Institution: | 1. Department of Mathematics, City University of Hong Kong, PR China;2. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, PR China;3. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, PR China |
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Abstract: | In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work 27], we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces. |
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Keywords: | 35A07 35M33 35Q35 76N20 76W05 Compressible MHD Boundary layers Non-monotonic velocity fields Local well-posedness |
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